Method and apparatus for extending flammability and stability limits in a combustion reaction

ABSTRACT

A method and apparatus for controlling a combustion reaction includes steps and structures for applying an electric field across a combustion reaction. Application of the electric field results in broadening the flammability and stability limits of the fuel.

CROSS REFERENCE TO RELATED APPLICATION

The present application is a U.S. Continuation-in-Part Application which claims priority benefit under 35 U.S.C. §120 of co-pending International Patent Application No. PCT/US2014/073086 entitled “METHOD AND APPARATUS FOR EXTENDING FLAMMABILITY LIMITS IN A COMBUSTION REACTION,” filed Dec. 31, 2014 (docket number 2651-203-04), co-pending herewith; which application claims priority benefit from U.S. Provisional Patent Application No. 61/922,430, entitled “METHOD AND APPARATUS FOR EXTENDING FLAMMABILITY LIMITS IN COMBUSTION REACTION,” filed Dec. 31, 2013 (docket number 2651-203-02); each of which, to the extent not inconsistent with the disclosure herein, is incorporated herein by reference.

BACKGROUND

Combustion requires fuel, such as hydrogen or a hydrocarbon gas; an oxidant such as oxygen carried in air, and an ignition source. For any given fuel, there is a range of fuel to oxygen ratios within which combustion can occur or be sustained. Flammability limits convey information about the minimum and maximum concentrations of the fuel that will sustain combustion under standard conditions. The flammability limits of the particular fuel, i.e., the lowest and highest ratios of fuel: oxygen at which the fuel is flammable, are determined under standard conditions (unless specifically defined otherwise). Typically, the standard conditions used for measuring the flammability limits for many fuels are 25° C. and one bar of pressure, absolute (100 kPa), with the oxidizer specified to be oxygen at nominal atmospheric concentration in air.

It is generally considered true that flammability limits are an intrinsic property of a fuel or fuel mixture. Flammability limits are expressed as a percentage of fuel within a volume of air. For example, the lower flammability limit of gasoline (100 octane) is 1.4%, i.e., a mixture containing 1.4% gasoline and 98.6% air. This is the lowest, or leanest concentration of gasoline that is combustible. At the other end of the range, the upper flammability limit of gasoline is 7.6%, representing the richest fuel concentration that is combustible.

Stability limits are analogous to flammability limits. Flammability limits are considered properties of the fuel—that is, a flammability limit is device-independent. Stability limits, by comparison, are the actual combustible limits realizable by a given device such as an actual burner or combustor. In industrial burners, stability limits often govern the safe operation of the burner. The lower stability limit is the most fuel-lean composition whose combustion a given burner can support, while the upper stability limit is the most fuel-rich composition whose combustion a given burner can support. In practical combustion equipment, the upper and lower stability limits define the stable combustion operating range for a given burner or combustion device.

SUMMARY

According to an embodiment, a method includes introducing fuel and air into a combustion volume in a first ratio that is outside a range of fuel concentrations between an upper stability limit and a lower stability limit, igniting the fuel, and producing a modified range of fuel concentrations defined by a modified upper stability limit and a modified lower stability limit of the fuel by applying an electric field across a flame supported by the fuel and air, wherein the first ratio is within the modified range.

According to an embodiment, a combustion system includes a burner configured to support a combustion reaction, first and second electrodes positioned and configured to apply an electric field across the combustion reaction supported by the burner, and a voltage supply, operatively coupled to the first and second electrodes, and configured to supply voltage signals to the first and second electrodes. In some embodiments, controller is configured to detect the combustion reaction, and to control the voltage supply to supply voltage signals to the first and second electrodes sufficient to produce a modified upper stability limit and/or a modified lower stability limit of the fuel to extend stability of the combustion reaction.

According to an embodiment, a method for controlling a combustion reaction includes receiving, via a data interface, a command to establish a particular fuel stability limit, reading data corresponding to a fuel parameter (such as pressure and/or temperature, for example), and determining, as a function of the data, (e.g., algorithmically calculating or looking up) second data corresponding to a signal selected to cause a particular voltage to be applied to a physical electrode operatively coupled to the combustion reaction. The second data is converted into the signal used to drive a voltage amplifier. The method further includes outputting from the voltage amplifier and transmitting to the electrode, electric current at the particular voltage. The applied electric field causes the fuel to combust at the particular stability limit responsive to exposure to the energized physical electrode.

According to an embodiment, a low NOx burner includes a physical flame holder configured to receive a particular fuel and oxidant mixture at a particular condition and an electrode configured to apply an electric field to the fuel and oxidant mixture, the electric field being selected to cause the fuel and oxidant to undergo a combustion reaction at the particular mixture. The fuel and oxidant are characterized by a leaner mixture than would react in combustion at the particular condition without being exposed to the electric field.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a combustion system, according to an embodiment.

FIG. 2 is a flow chart depicting a method of operation of a combustion system, according to an embodiment.

FIG. 3 is a diagram showing elements of a test system employed by the inventors to investigate and prove principles described and claimed herein, according to an embodiment.

FIG. 4 is a ternary mixture diagram depicting three fuels in experimental mixture space, according to an embodiment.

FIGS. 5A-5B are ternary diagrams illustrating the widening of flammability limits in the ternary hydrogen-methane-propane (H₂—CH₄—C₃H₈) mixture space in the presence of an electric field, according to an embodiment.

FIGS. 6A-6C are ternary diagrams showing the contours for flammability limit changes determined by experiment, according to an embodiment.

FIG. 7 is a graph showing enhancement of rich flammability limits, according to an embodiment.

FIGS. 8A-8B are ternary diagrams showing percent change contours for lean and rich flammability limits per equations, according to an embodiment.

DETAILED DESCRIPTION

In the following detailed description, reference is made to the accompanying drawings, which form a part hereof. In the drawings, similar symbols typically identify similar components, unless context dictates otherwise. Other embodiments may be used and/or other changes may be made without departing from the spirit or scope of the disclosure.

As used herein, the term lower flammability limit (LFL) refers to the leanest concentration of a given fuel (such as a fuel mixture, for example) in air that is combustible under standard measurement conditions. The term lower stability limit (LSL) refers to the leanest concentration of the given fuel that is combustible under actual operating conditions for a particular burner. Upper flammability limit (UFL) refers to the richest concentration of a given fuel in air that is combustible under standard measurement conditions. Upper stability limit (USL) refers to the richest concentration of the given fuel that is combustible under actual operating conditions of a particular burner.

The terms modified lower flammability limit (MLFL) and modified upper flammability limit (MUFL) (which may be collectively referred to using the term modified flammability limit (MFL)) are used to refer to the respective flammability limits as modified using the structures and methods described hereafter. The terms modified lower stability limit (MLSL) and modified upper stability limit (MUSL) (or, collectively, modified stability limit (MSL)) are used to refer to the respective stability limits as modified using the structures and/or methods disclosed hereafter. To avoid confusion and for economy of language, the terms stability limit(s) and flammability limit(s) may be used interchangeably.

The terms combustion, combustion reaction, and flame may be used interchangeably herein, and shall be regarded as equivalent unless context dictates otherwise.

As used herein, the term fuel shall be understood to include a fuel mixture (i.e., a mixture including two or more pure fuels) unless context indicates otherwise.

Other terms that are related to, or synonymous with terms defined above may also be used hereafter, the meanings of which will be clear in view of the context.

It has been long understood in the art that flammability limits of any given fuel are substantially immutable. Tables setting forth the flammability limits of selected or common fuels can be found in many combustion engineering texts and general references. Such tables are relied upon by designers of combustion systems when calculating the parameters of individual system components to ensure that systems perform as intended.

The inventors have discovered that parameters describing combustion stability limits in a furnace system can be driven to diverge from corresponding flammability limits of many fuels. In particular, combustion can be made more stable by applying an electric field to the combustion reaction. The inventors discovered that the stability limits of combustion equipment were expanded by applying an electric field to the flame.

When an electric field is present across a flame, the LFL and UFL of the particular fuel or mix of fuels no longer represent the flammability limits of the particular fuel or mix of fuels. The application of an electric field creates a MLFL that is lower (i.e., leaner) than the LFL, and a MUFL that is higher (i.e., richer) than the UFL. The degree to which the stability limits are modified varies according to the particular fuel and the strength of the electric field.

As previously noted, flammability limits are generally expressed as values corresponding to specific standard temperatures and pressures. As the temperature and/or pressure changes, the stability limits diverge from published flammability limits at standard conditions. Many combustion systems are configured to operate at pressures and/or temperatures that are far removed from the standard conditions associated with the standard tables. Furthermore, many combustion systems are not configured to operate using a mix of air and fuel, but instead employ other oxidizers, or may further dilute the oxygen by introducing recirculated flue gas, etc. Nevertheless, the stability limits of a given fuel can be calculated for any reasonable combination of temperature, pressure, and oxygen concentration. Thus, the applicable standard flammability limits are considered to apply, as revised, to accommodate the varied conditions of individual burners.

The inventors found that experimental results related to upper and lower flammability limits (UFL, LFL) and modified upper and lower flammability limits (MUFL, MLFL) at standard conditions are predictive of upper and lower stability limits (USL, LSL) and modified upper and lower stability limits (MUSL, MLSL) in given burners.

FIG. 1 is a diagram showing a combustion system 100, which is configured to modify the stability limits of fuels or mixes of fuels, according to an embodiment. The combustion system 100 includes a burner 102 and a combustion control system 104. The burner 102 is configured to support a combustion reaction 106, and includes a fuel nozzle 108, an oxidizer conduit 110, a fuel source 112, and an oxidizer source 114. The fuel source 112 and oxidizer source 114 are coupled to the fuel nozzle 108 and oxidizer conduit 110, respectively, via corresponding transmission conduits 116. The fuel source 112 and oxidizer source 114 are each configured to be controllable to regulate the volume or flow rate of fuel and oxidizer, respectively. Optionally, the oxidizer source 114 may include a forced draft (blower) system.

The fuel source 112 and oxidizer source 114 can be arranged in any of a large number of configurations, depending upon factors such as, for example, the size, capacity, intended purpose, complexity, and projected duty cycle of the combustion system 100. Additionally, in many cases, the combustion system may be subject to governmental regulations relating to emissions, which further affect the design of the system. According to an embodiment, the oxidizer source 114 can be configured to control oxygen input and/or air temperature by introducing recirculated flue gas. According to an embodiment, the burner 102 is configured to premix fuel and air, then to emit the mixture from the nozzle 108. According to another embodiment, the fuel is ejected with some force from the nozzle 108 in a form that entrains air from the oxidizer conduit 110. According to an alternate embodiment, the oxidizer is forced into the combustion volume with a blower. According to some embodiments, only one of the fuel or oxidizer is regulated, the other being supplied at a substantially constant rate.

According to an alternative embodiment, the fuel and oxidizer are premixed to a selected mixture, and the combustion reaction 106 is supported by the premixed fuel and oxidizer. In an embodiment, fuel and oxidizer are premixed to a selected mixture that falls outside the normal stability limits of the fuel. As will be appreciated, a mixture of fuel and oxidizer that is outside the stability limits is nominally non-combustible. Such a mixture can be considered a safe mixture because a flame will not propagate into a mixer containing the mixture. According to an embodiment, the mixture combusts only where and when the mixture is exposed to an appropriate electric field.

According to an embodiment, a mixture of fuel and oxidizer is ejected from the burner 102 at a ratio that is below the LSL of the fuel, i.e., too lean to maintain combustion. An electric field is applied as described in more detail below. Application of the electric field produces a MLSL that is below the current ratio, rendering the mixture combustible, but only while the electric field is present. Removal of the field again renders the mixture non-flammable. As the mixture flows from the burner 102, it can only become leaner, and thus cannot become flammable absent the electric field. In an embodiment, a failsafe is thus provided, significantly reducing the danger of accidental combustion.

The combustion control system 104 includes first and second electrodes 118, 120 and a voltage source 124. In some embodiments, the combustion control system 104 includes a control unit 128 and one or more sensors 122 operatively coupled to the control unit. The first electrode 118 is positioned downstream from the burner 102 adjacent to the combustion reaction 106. A surface of the burner nozzle 108 can be operatively coupled to the voltage source for operation as the second electrode 120. Connectors 130 couple the voltage source 124 to the first and second electrodes 118, 120. In some embodiments, an electrode 120 may carry chassis and/or earth ground, and a connector 130 may be replaced by conductive structures of the burner 102. Various interfaces including physical connector(s) and wireless interface(s) can be used to couple the control unit 128 to the sensor 122. Connectors (or wireless interfaces) may optionally couple control signals from the control unit 128 to the voltage source 124, the fuel source 112, and the oxidizer source 114.

The voltage source 124 is configured to apply a voltage difference across the combustion reaction 106 via the first and second electrodes 118, 120. The sensor 122 represents one or more individual sensors, each configured to measure one or more characteristics of the combustion reaction 106 and to supply corresponding signals to the control unit 128. For example, the sensor 122 can be configured to measure characteristics such as temperature, oxygen concentration, luminosity, combustion byproducts, electrical charge, etc.

Structures configured to electrically connect components or assemblies shown in the drawings are depicted generically as connectors 130, inasmuch as electrical connectors and corresponding structures are very well known in the art, and equivalent connections can be made using any of a very wide range of different types of structures. The connectors 130 can be configured to carry high-voltage signals, data, control logic, etc., and can include single conductors or multiple separately-insulated conductors. Additionally, where a voltage potential, control signal, feedback signal, etc., is transmitted via intervening circuits or structures, such as, for example, for the purpose of amplification, detection, modification, filtration, rectification, etc., such intervening structures are considered to be incorporated as part of the respective connector.

In an embodiment, fuel is supplied and regulated to the fuel nozzle 108 by the fuel source 112, while the oxidizer is similarly supplied and regulated by the oxidizer source 114. The control unit 128 monitors selected parameters or characteristics of the combustion reaction 106, and may control the fuel source 112 and oxidizer source 114 to keep the selected characteristics within defined limits. Additionally or alternatively, various aspects of the combustion reaction 106 can be controlled by application of electrical energy via the first and/or second electrodes 118, 120. When the control unit 128 receives sensor signals indicating that the combustion reaction 106 is operating near its upper or lower stability limit, the control unit 128 is configured to control other elements of the combustion system 100 to bring operation of the combustion reaction to a point farther removed from the stability limits, or to modify the stability limits to be farther from the current point of operation.

For example, the control unit 128 may detect that the combustion reaction 106 is unstable, or that it repeatedly blows out, requiring periodic re-ignition; or the control unit 128 may determine that a leaner fuel/air mixture is required in order to obtain a selected emissions value, which results in producing an unstable flame, etc.

In an embodiment, upon detection of operation at a fuel/air ratio that approaches the LSL or USL (or previously applied MLSL or MUSL) of the combustion reaction 106, the control unit 128 is configured to control the voltage source 124 to apply or modify a voltage difference across the combustion reaction 106, via the first and second electrodes 118, 120, in order to establish an electric field across the flame. The magnitude of the voltage difference to be applied can be determined by reference to a lookup table or by calculation based on the fuel type, degree of desired modification of the stability limits, and/or on other predetermined factors. Additionally or alternatively, the control unit 128 can be configured to control the voltage source 110 to adjust the magnitude upward until signals from the sensor 122 indicate that the combustion reaction 106 is in a stable operation state.

FIG. 2 is a flow chart depicting a method of operation 200 for controlling a combustion reaction, according to an embodiment. At 202, a fuel/air mixture is supplied to a combustion reaction. This will typically be in the form of a fuel and air mixture, but can include any appropriate oxidizer, and can include other known components that affect the fuel to oxygen ratio, including, for example, recirculated flue gas.

At 204, a determination is made whether the fuel/air ratio of the mixture is outside the range defined by the stability limits. If the determination is made that the ratio is within the range (the NO path), the process returns to step 202, at which the fuel/air mixture continues to be supplied to the combustion reaction.

If, at step 204, it is determined that the fuel/air ratio is outside the stability limit range (the YES path), the process proceeds to step 206, where the stability limits are modified by application of an electrical field across at least a portion of the combustion reaction. Following step 206, the process returns to step 202 and repeats.

According to an embodiment, step 206 can include selecting an adequate magnitude of the electric field to modify the stability limits to a degree sufficient to encompass the current fuel/air ratio. According to an alternative embodiment, the magnitude of the electric field is increased incrementally with each repetition of the cycle, so that multiple cycles of the process may be required before the stability limits have been sufficiently modified.

According to a further embodiment, the process can include a step in which a previously applied electric field is reduced incrementally each time the NO path is taken from step 204, or, alternatively, after a predetermined number of times that the NO path is taken. In this way, the strength or magnitude of the electric field is maintained near the minimum value necessary for proper operation, and the electric field is removed when no longer necessary.

Examples

FIG. 3 is a diagram showing elements of a test system 300 used by the inventors in experiments performed to demonstrate the principles described with reference to embodiments described herein. The test system 300 included a burner 302, a fuel/air control system 304, and a combustion control system 306.

The burner 302 included a sintered bronze plate 308, a cooling coil 310, and a plenum chamber 312 defined by a plenum chamber wall 313. The bronze plate 308 was porous, configured to permit fuel and air to pass from the plenum chamber 312 below the plate 308 to an upper side of the plate 308. A quartz cylinder 314 was positioned above and surrounding the bronze plate 308. The cooling coil 310 included a coolant inlet 316 and a coolant outlet 318. During operation of the test system, water was pumped through the cooling coil 310 to control the temperature of the bronze plate 308, and to prevent transmission of heat from a combustion reaction 320 above the plate 308 to the plenum chamber 312, below the plate 308. A fuel inlet 322 was provided to permit introduction of a fuel/air mixture into the plenum chamber 312.

The fuel/air control system 304 included fuel sources A, B, and C, each configured to provide a respective fuel. An air source 324 was also provided. A respective valve/flow meter 326 a-d was associated with each of the fuel sources A, B, and C, and the air source 324. The air source 324 and each of the fuel sources A, B, and C were coupled, via their respective valve/flow meter 326 a-d, to a mixer 328, which was in turn coupled via a master valve/flow meter 326 e to the fuel inlet 322.

The combustion control system 306 included a voltage supply 330 operatively coupled to a stainless steel mesh electrode 332 positioned above the quartz cylinder 314. The voltage supply 330 was also coupled to the bronze plate 308, and was configured to apply a voltage difference between the electrode 332 and the bronze plate 308.

During operation of the tests, the inventors controlled the valve/flow meters 326 a-d to regulate the type and mixture of fuel, and the ratio of fuel to air. The fuel and air were mixed in the mixer 328, and the total volume of fuel and air mixture 334 introduced into the plenum chamber 312 was controlled by the master valve/flow meter 326 e. The mixture 334 was ignited as it passed through the bronze plate 308, and the tests were conducted as described in detail below. The inventors observed that a modest electric field significantly widened stability limits for hydrogen-methane-propane (H₂—CH₄—C₃H₈) fuel blends simulating refinery fuel gas. Observed stability limits were mathematically modified to standard conditions to calculate flammability limits. The lean flammability limit was decreased by between 2.7% and 5.9%, depending on the fuel blend. The rich flammability limit was increased by between 5.6% and 14.1%, depending on the fuel blend. Overall widening of the flammability limits was 8.5% to 20.3%, depending on the fuel blend.

The upper flammability limit correlated well with the square root of the molar hydrogen to carbon ratio H/C in the fuel (r²=99.0%). Modification of the upper flammability limit may accrue from better transport of the oxidizing species from combustion air under the influence of the electric field. One possible explanation for this may be an attraction of hydronium ions (H₃O⁺) from the air to the grounded nozzle, causing an increase in hydroxide ion concentration [OH-] delivered to the flame. This, in turn, would enhance carbon monoxide (CO) oxidation: CO+OH=CO₂+H, and thus the overall reaction rate of the hydrocarbons.

The inventors observed a change in the lower flammability limit (to the MLFL) of about half of that of the modified upper flammability limit. Possibly, this is due to the presence of CO in much lower concentration in lean flames; therefore, the enhancement of CO oxidation is presumably less beneficial. The change in the lower flammability limit also correlates negatively with the C₃H₈ concentration (r²=99.0%) and to a much lesser extent with the addition of H₂ concentration (or positively to CH₄ addition) to the model (r²=99.98%).

As to propane's effect, one possibility is that C₃H₃ ⁺ impeded oxidation at the lower flammability limit (see Section 5, Conclusions). Since C₃H₃ ⁺ correlates with C₃H₈ concentration, this effect would be more pronounced with propane-rich fuels. The reason that an increase in the hydrogen concentration slightly reduced the relative widening of the lean limit is less clear. One possibility is that at the lean limit H₂ scavenges OH generated by H₃O⁺. Another possibility is that CH₄ is actually the important moiety (and as C₃H₈ increases, H₂ must, from mathematical necessity, decrease in a ternary mixture).

Flammability and stability limits were found to be significantly widened in an electric field.

Apparatus

The apparatus included a 51 mm diameter sintered bronze disk through which a premixed fuel and air mixture flowed. An added quartz tube atop the burner isolated the flame from the surroundings. The quartz tube had an inner diameter of 56 mm. A circular stainless steel screen electrode was positioned 8 mm above the quartz tube. An electric potential between the screen electrode and the flame was maintained at 10 kV, generating an electric field of 1.2 kV/cm. Cooling water was used to stabilize the flame.

A circular stainless steel screen electrode was placed above the quartz tube resting on an electrically grounded burner. Hydrogen, methane, propane, and air were individually fed through four OMEGA™ thermal flow meters (not shown, available from Omega Engineering, Inc., Stamford Conn., USA) to generate the desired fuel flow rates. Each meter was electrically floated with an inverter and a battery so as to keep the meters from being shocked by high voltage. The gases were then blended and controlled by valves downstream of the fuel blend but upstream of the burner (not shown). The valve panel was grounded for safety. The fuels were fed from a tank farm; air was fed from an air compressor. Ambient humidity was neglected in the calculations (and constituted about 1% of the air by volume).

Procedure

To investigate the LFL and UFL (and MLFL and MUFL), the fuel feed was held constant while increasing or decreasing the airflow until reaching blowout. In the case of the UFL and MUFL, the airflow was decreased so as to make the mixture more fuel rich. In the case of the LFL and MLFL, the airflow was increased so as to make the mixture more fuel lean. Blowout was defined as the condition where the flame blew completely out of the quartz tube. The blowout limit was determined without electric field under constant fuel flow before testing with electric field application. While the burner could withstand higher flows, the airflow meter had a maximum 50 SLPM capacity. Thus, the airflow was set to 80% of maximum (to give some margin for leaner limits under an electric field) and then decreased the fuel to give the maximum lean condition. The airflow was then reduced, the burner was relit, and an electric field was applied. Airflow was increased until blowout occurred. In all cases, a reduction in LFL and LSL was achieved when an electric field was applied. For the upper flammability (fuel-rich) limit, the airflow was reduced little by little until the flame blew out. This procedure was then repeated under the influence of an electric field. In all cases, the application of an electric field yielded higher UFL and USL.

Data and Results

Table 1 shows properties of the tested fuels and mixtures. The tested fuel mixtures had a maximum of 50% hydrogen concentration. In Table 1, H/C is the molar hydrogen to carbon ratio in the fuel, LHV is the lower heating value in BTU/scf, AFT is the adiabatic flame temperature, Φ is the stoichiometric fuel/air mixture ratio, τ is the theoretical fuel/air mixture ratio (defined at stoichiometric ratio Φ=1), %. Fuel is the volume fuel concentration in the fuel/air mixture, LL is the (fuel-lean) lower flammability or stability limit in terms of the percent of fuel in the fuel/air mixture, and RL is the (fuel-rich) upper flammability or stability limit expressed on the same basis. In Table 1, no electric field has been applied and the UFL and LFL represent native fuel properties as measured by the apparatus. Such limits show good general agreement with literature values for flammability limits despite literature values being measured in more exacting apparatuses.

TABLE 1 Fuel and Mixture properties Fuel Fuel/Air Mixture Properties Composition Properties Φ = 1 Flammability Code H₂ CH₄ C₃H₈ H/C LHV AFT τ % Fuel LL, % RL, % 0-100-0 0 100 0 4.00 912 2223 9.52 9.50 5.2 14.4 0-0-100 0 0 100 2.67 2385 2265 23.81 4.03 2.4 8.7 0-50-50 0 50 50 3.00 1649 2244 16.67 5.66 3.1 10.9 50-50-0 50 50 0 6.00 593 2346 5.95 14.38 4.8 19.9 50-0-50 50 0 50 3.33 1330 2369 13.10 7.09 2.8 13.1 25-50-25 25 50 25 3.60 1121 2294 11.31 8.12 3.7 13.9

FIG. 4 is a ternary mixture diagram depicting the fuels in experimental mixture space, according to an embodiment. The circles show the experimental blends that were investigated. Hydrogen blends above 50% were not investigated. Table 2 shows fuel flammability limits (LFL, UFL) and modified flammability limits (MLFL, MUFL) respectively without and with the presence of an electric field, E, of 1.2 kV/cm field strength.

TABLE 2 Flammability Limits With and Without an Electric Field Composition E = 0 kV/cm E = 1.2 kV/cm Change, χ Code H₂ CH₄ C₃H₈ LFL, % RFL, % MLFL, % MUFL, % Lean % Rich % Total, % 0-100-0 0 100 0 5.1 14.4 4.8 15.8 −5.9 9.9 18.5 0-0-100 0 0 100 2.3 8.7 2.2 9.2 −2.7 5.6 8.5 0-50-50 0 50 50 3.1 10.9 3.0 11.6 −3.5 7.3 11.7 50-50-0 50 50 0 4.8 19.9 4.6 22.7 −5.6 14.1 20.3 50-0-50 50 0 50 2.8 13.1 2.7 14.3 −3.2 8.9 12.1 25-50-25 25 50 25 3.7 13.9 3.6 15.2 −4.3 9.4 14.5

From inspection, one sees that the LFL/MLFL and UFL/MUFL differ for the electric field off (0 kV/cm) and on (1.2 kV/cm); for example, the lean flammability limit for methane (first row) decreased from 5.1% methane to 4.8%, and the rich flammability limit increased from 14.4 to 15.8%. In general, the effect of the electric field was to widen the flammability limits for all fuels and blends with the lean limit becoming leaner and the rich limit becoming richer. In order to compare lean and rich limits, the inventors defined a change parameter (χ_(r), χ_(l)), per Equation 1.

$\begin{matrix} {{{_{r} = {{\frac{\lambda_{r,e}}{\lambda_{r}} - 1} = \frac{\lambda_{r,e} - \lambda_{r}}{\lambda_{r}}}};{_{l} = {{\frac{\lambda_{l,e}}{\lambda_{l}} - 1} = \frac{\lambda_{l,e} - \lambda_{l}}{\lambda_{l}}}}},} & (1) \end{matrix}$

where χ_(r), χ_(l) are the fractional change of the rich and lean limits, respectively, λ_(r,e), λ_(l,e) are the modified flammability limit (rich or lean, respectively) expressed as the fuel fraction in the presence of the electric field, and λ_(r), λ_(l) are the flammability limits with no electric field.

Under this definition, widening of the lean limit is negative while widening of the rich limit is positive. To calculate a total widening over the entire range, the inventors modified Equation (1) as follows.

$\begin{matrix} {{_{T} = {{\frac{\lambda_{r,e} - \lambda_{l,e}}{\lambda_{r} - \lambda_{l}} - 1} = \frac{\left( {\lambda_{r,e} - \lambda_{r}} \right) + \left( {\lambda_{l} - \lambda_{l,e}} \right)}{\lambda_{r} - \lambda_{l}}}},} & (2) \end{matrix}$

where χ_(T) is the total fraction of change in the flammability or stability range (rich minus lean) with and without electrical charge, λ_(r,e) is the MUFL (modified rich limit) in the presence of the electric field, λ_(r) is the UFL (rich limit) in the absence of the electric field, λ_(l,e) is the MLFL (modified lean limit) in the presence of the electric field, and λ_(l) is the LFL (lean limit) in the absence of the electric field.

FIGS. 5A-B depict two ternary diagrams illustrating the widening of flammability limits in the ternary H₂—CH₄—C3H₈ mixture space in the presence of an electric field, according to an embodiment. A modest electric field significantly widened flammability limits. The ternary diagram in FIG. 5A shows the normal (no electric field) flammability limits that were measured at each point in the mixture space. The ternary diagram in FIG. 5B shows wider flammability limits in the presence of an electric field with the MLFL (lean flammability limit) being leaner than the LFL and the MUFL (rich flammability limit) being richer than the UFL.

Analysis

Contour lines for six fuel blends can be fit exactly with a mixture model of the form

$\begin{matrix} {{y = {{\sum\limits_{k = 1}^{3}\; {c_{k}z_{k}}} + {\sum\limits_{j < k}^{2}{\sum\limits_{k = 1}^{3}\; {c_{jk}z_{j}z_{k}}}}}},} & (3) \end{matrix}$

where y is the response of interest (e.g., lower or upper flammability limit), j,k are indexes for the three fuel components (1≦j<k≦2; 1≦k≦3), z_(j)z_(k) are the fuel components i.e., z₁=H₂, z₂=CH₄, z₃=C₃H₈.

${{\sum\limits_{k = 1}^{3}\; z_{k}} = 1},$

because the fuel components must sum to 100%, c_(k), c_(jk) are the associated coefficients for the pure components and blends (c₁, c₂, c₃, and c₁₂, c₁₃, c₂₃, respectively).

Note that Equation (3) contains no error term, nor is it possible to deduce one, as six mixture points will determine six coefficients with certainty.

FIGS. 6A-C depict three ternary diagrams showing the contours for flammability limit changes deduced in this way, according to an embodiment. The series shows percent changes in flammability or stability limits in ternary mixture coordinates. The diamonds indicate the data points, with actual percent changes indicated above each point. In FIG. 6A, the lines and negative values indicate the percent change in lean limits. In FIG. 6B, the lines and positive values indicate the percent change in rich limits. FIG. 6C gives the contours for total percent change over the entire range. Overall, a 1.2 kV/cm electric field widened limits between 8.5 and 20.3%, depending on the fuel. Because of the way these contours were derived they are purely empirical and agree exactly with the values of the data set.

In order to perform statistical tests the number of coefficients must be less than the number of fuel blends tested; that is, fewer than six and preferably only two or three. Equations (4) and (5) satisfy the rich and lean change fractions, respectively.

χ_(r) ² =a ₀ +a ₁ x+ε  (4)

χ_(l) =b ₀ +b ₁z₁ +b ₃z₃ +b ₃₃z₃ ²+ε  (5)

where χ_(r), χ_(l) are the fractional change in the rich and lean limits, respectively, x is the H/C ratio of the fuel, z₁ is the fraction of H₂ in the fuel, z₃ is the fraction of C₃H₈ in the fuel, a₀₋₂, b₀₋₃₃ are the respective coefficients, and ε is the error term.

The rich limits were found to be a function of H/C ratio alone. The model has the following statistics.

TABLE 3 ANOVA for Equation (4) Source DF SS MS F p Model 1 16,373 16373 381.3 <.0001 Residual 4 172 42.9 r² 0.990 Total 5 16,545 361.4 r_(p) ² 0.978

Table 3 shows the analysis of variance (ANOVA) for equation (4). The model contains 1 degree of freedom (DF), leaving 4 DF to estimate the error, and thus comprising a total of 5 degrees of freedom. In actuality, the model may be said to contain 2 degrees of freedom: a₀, and a₁; however, if the model were not significant—termed the null hypothesis—then all data points are replicates and would be best expressed by a mean value. Since the null hypothesis contains 1 degree of freedom (the mean) it is subtracted from the degrees of freedom of the model to give a net 2 degrees of freedom, which is what is reported in the analysis of variance table. Furthermore, it may be said that there are actually 6 DF for the model corresponding to the six data points collected. However, if the model was not significant, one would average all six values with a single mean. Since the mean represents 1 degree of freedom, the net amount of degrees of freedom is actually 5.

Table 3 entries have the following meanings: the sum of squares (SS) column shows the variance proportional to each respective source of variance. If the model were to fit the data exactly, it would be equal to the Total SS with zero Residual SS. The mean square (MS) column is derived by dividing the SS column by the DF column, excluding the bottom number, which will be discussed later. The ratio of Model MS with the Residual MS gives an F ratio—in this case of 381.3. If the model were no better at explaining the variance than chance, F would be ˜1. Since 381.3>>1, the model is statistically different from chance deviation. The probability, p, that the F ratio is significant is given by the value p<0.0001. Thus, the F ratio of 381.3 is estimated to occur by chance less than 1 time in 10,000. In other words, the model is statistically significant with >99.99% certainty (1−0.0001=0.9999). Generally, a model is considered statistically significant if p<0.05, which is the case here. r² is the ratio of the Model SS/Total SS. If the model fits the data exactly the r²=1, and the model explains 100% of the data variation. In the present case, r²=0.990; that is, the model explained 99.0% of the total variation. The bottom number is the PRESS statistic (predicted sum of squares). It is not derived from the ANOVA, but it may be used to make an inference about the predictive power of the model (as opposed to the correlative power of the model given by r²). A predictive estimate, r_(p) ², was calculated by subtracting from 1 the ratio of PRESS/Total SS. In this case r_(p) ²=0.978 and infers that model is likely to have good predictive power. With knowledge that the model is statistically significant, the data was examined further to derive coefficient estimates for each of the model terms (Table 4).

TABLE 4 Statistics for Equation (4) Term Est Std Err t ratio p a₀ −90.28 9.67 −9.34 0.0007 a₁ 48.178 2.47 19.53 <.0001

The Table 4 entries have the following meaning: The Term shows the respective coefficients for Equation (4). The estimate column (Est) gives the least squares value for each coefficient. The standard error (Std Err) gives the uncertainty of the associated coefficient. For example, a₀ is estimated to be −90.28±9.67. Thus the estimate was many times larger than the standard error and was likely to be statistically significant. The t ratio column is the estimate divided by the standard error. One prefers to see |t|>>1 as is the case here. The p value gives the probability that a particular t ratio may occur by chance. For a₀, the p value is 0.0007, meaning there is merely a 0.07% probability that a t ratio of −9.34 may occur by chance. In general, the inventors rejected the null hypothesis if p<0.05, as is the case here.

FIG. 7 is a graph showing that the enhancement of the rich limits correlated well with square root of the H/C ratio (Equation 4), according to an embodiment.

Tables 5 and 6 give the associated statistics for Equation 5.

TABLE 5 ANOVA for Equation (5) Source DF SS MS F p Model 3 8.7047 2.9016 3243.4 0.0003 Residual 2 0.0018 0.0009 r² 0.9998 Total 5 8.7065 0.1553 r_(p) ² 0.9822

TABLE 6 Statistics for Equation (5) Term Est Std Err t ratio p VIF b₀ −5.449 0.0264 −206.69 <.0001 b₁ 0.596 0.0597 9.97 0.0099 1.20 b₃ 4.013 0.0416 96.4 0.0001 1.39 b₃₃ −3.120 0.1099 −28.4 0.0012 1.44

All of the model coefficients are statistically significant at p<0.05, both the correlation coefficient and the predictive coefficient are very close to 1. The variance inflation factor (VIF) characterizes the correlation among factor variables. If there is no correlation (desired) then VIF=1. The relationship between VIF and r² is r²=1−1/VIF. Thus, VIFs of 1.20, 1.39, and 1.44 correspond respectively to r²s of 0.167, 0.281, and 0.306—all quite meager, meaning that the factor disposition is well dispersed in mixture space with little collinearity. Equation (5) generates the contours shown in FIGS. 8A-B.

FIGS. 8A-B depict two ternary diagrams showing the percent change contours for lean and rich flammability limits per equations (5) and (4), according to an embodiment. FIG. 8A shows the percent decrease in the lean limits as a function of mixture fraction based on Equation (5). FIG. 8B shows the increase in rich limits according to Equation (4). In general, the contours compare well to the exact contours (FIG. 6).

CONCLUSIONS

Flammability limits can be defined as “the state at which steady propagation of the planar premixed flame . . . fails to be possible.” It has been long known that increased temperature widens flammability limits. Increased pressure also widens flammability limits because it increases the fuel and oxygen concentrations. Increases in oxygen concentration widen flammability limits, particularly on the rich side because the additional oxygen can react under rich conditions, whereas on the lean side oxygen is not the limiting reagent. If an electric field enhances the fuel concentration at the lean side or the oxidant concentration on the rich side, then it would likewise widen the overall flammability limit.

Two facts are now apparent. The rich limit widens in direct proportion to the square root of the H/C molar ratio. The lean limit widens in opposition to the C₃H₈ concentration and to a lesser extent with the hydrogen concentration.

While various aspects and embodiments have been disclosed herein, other aspects and embodiments are contemplated. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims. 

What is claimed is:
 1. A method, comprising: introducing fuel and air into a combustion volume in a first ratio that is within a first range defined by an upper stability limit and a lower stability limit of the fuel; igniting the fuel to start a combustion reaction; producing a modified range defined by a modified upper stability limit higher than the upper stability limit and a modified lower stability limit lower than the lower stability limit of the fuel by applying an electric field across the combustion reaction; and after igniting the fuel and after producing the modified range, adjusting a flow rate of the fuel or air to produce a second ratio within the modified range and outside the first range.
 2. The method of claim 1, further comprising: prior to producing the modified range, monitoring one or more characteristics of the combustion reaction; and detecting values of the one or more monitored characteristics that indicate a requirement that the ratio of fuel and air be adjusted from the first ratio to the second ratio, wherein producing the modified range is performed in response to detecting values of the one or more monitored characteristics.
 3. The method of claim 1, wherein applying the electric field modifies an upper flammability limit and a lower flammability limit of the fuel.
 4. A combustion system, comprising: a burner configured to support a combustion reaction by emitting fuel and oxidizer; first and second electrodes positioned to apply an electric field across the combustion reaction; and a voltage supply operatively coupled to the first and second electrodes, and configured to supply voltage signals to the first and second electrodes sufficient to cause the electric field to produce a modified upper stability limit higher than a normal upper stability limit of the fuel and a modified lower stability limit lower than a normal lower stability limit of the fuel.
 5. The system of claim 4, wherein the first electrode comprises a fuel nozzle portion of the burner.
 6. The system of claim 4, wherein the second electrode comprises a mesh electrode positioned above the burner.
 7. The system of claim 4, further comprising: a controller configured to detect operation of the burner and to control the voltage supply to supply voltage signals to the first and second electrodes sufficient to produce the modified upper stability limit and the modified lower stability limit of the fuel.
 8. A method for controlling a combustion reaction, comprising: receiving, via a data interface, a command to establish a particular fuel stability limit; reading data corresponding to a fuel parameter; determining, as a function of the data, a particular voltage to be applied to a physical electrode operatively coupled to a combustion reaction; applying the particular voltage to the physical electrode; and causing the fuel to combust at a mixture within the particular stability limit responsive to an electric field generated by application of the particular voltage to the physical electrode.
 9. The method for controlling a combustion reaction of claim 8, wherein determining the particular voltage includes determining second data corresponding to the particular voltage.
 10. The method for controlling a combustion reaction of claim 9 wherein determining the particular voltage includes: converting the second data into a signal; driving a voltage amplifier with the signal; and outputting the particular voltage from the voltage amplifier to the electrode.
 11. The method for controlling a combustion reaction of claim 9, wherein determining the second data includes algorithmically calculating the second data.
 12. The method for controlling a combustion reaction of claim 9, wherein determining the second data includes looking up the second data.
 13. The method for controlling a combustion reaction of claim 8, wherein the fuel parameter includes ambient pressure.
 14. The method for controlling a combustion reaction of claim 8, wherein the fuel parameter includes ignition temperature.
 15. A low NOx burner, comprising: a physical flame holder configured to receive a fuel and oxidant mixture at a particular condition; and a first and second electrode configured to apply an electric field to the fuel and oxidant mixture, wherein the fuel and oxidant are characterized by a leaner mixture than would stably combust at the particular condition without being exposed to the electric field.
 16. The burner of claim 15, wherein the particular condition includes a temperature proximate to the physical flame holder.
 17. The burner of claim 15, wherein the particular condition includes atmospheric pressure proximate to the physical flame holder.
 18. A method, comprising: introducing fuel and air into a combustion volume in a first ratio that is outside a range defined by an upper stability limit and a lower stability limit of the fuel; producing a modified range defined by a modified upper stability limit and a modified lower stability limit of the fuel by applying an electric field across the fuel and air, the first ratio falling within the modified range; and after producing the modified range, igniting the fuel.
 19. The method of claim 18, further comprising: prior to producing the modified range, monitoring one or more characteristics of the fuel and air; prior to producing the modified range, detecting values of the one or more monitored characteristics that indicate that the first ratio of the fuel and air is at or above the upper stability limit or the lower stability limit; and producing the modified range after the monitoring and the detecting.
 20. The method of claim 18, wherein producing a modified range includes: determining a magnitude of the electric field to be applied, based at least in part on a value of the first ratio and a value of one of the upper stability limit or the lower stability limit; and applying the electric field at the determined magnitude.
 21. The method of claim 19, wherein the producing a modified range includes: applying the electric field at a preselected magnitude; repeating the monitoring and the detecting; and increasing the magnitude of the applied electric field by a preselected increment. 